let V be ComplexLinearSpace; :: thesis: for V1 being Subset of V st V1 is Coset of (Omega). V holds
V1 = the carrier of V
let V1 be Subset of V; :: thesis: ( V1 is Coset of (Omega). V implies V1 = the carrier of V )
assume V1 is Coset of (Omega). V ; :: thesis: V1 = the carrier of V
then ex v being VECTOR of V st V1 = v + ((Omega). V) by Def12;
hence V1 = the carrier of V by Th65; :: thesis: verum